Tonneau covers are generally used to cover the cargo box of a vehicle, such as a pick-up truck. A typical tonneau cover includes a cover sheet made of a flexible, waterproof material, and a frame structure to which the cover sheet is removably attached. Such tonneau cover assemblies can be problematic. For example, such frame structures often extend into the cargo space, and some covers can be opened from the exterior of the cargo box even with the tailgate closed. Additionally, sealing of the cargo box from water may be problematic.